The present disclosure provides computing systems in which respective quorums of computing nodes securely manage respective secrets associated with cryptographic ledgers according to threshold secret sharing schemes. In particular, membership in the quorums can be changed dynamically and unpredictability to improve security of the quorums against adversarial attacks in which adversaries attempt to compromise or gain control of the computing nodes. More specifically, by changing membership in the quorum dynamically and unpredictability, the ability of the adversary to control at any given time a threshold number of the current members of the quorum and gain access to the secret is dramatically reduced.